Page 304 - Sustainable On-Site CHP Systems Design, Construction, and Operations

Sustaining Operational Ef ficiency of a CHP System 277

where m = mass flow rate of fuel into the prime mover
Fuel
v Fuel = volumetric flow rate of the fuel
LHV and ρ = lower heating value and density of the fuel, respectively, evaluated
Fuel Fuel
at the input conditions
Combining Eqs. (17-2) and (17-3), the electric generation efficiency can be expressed
in terms of measurable variables as
W
η = elec (17-4)
EE m LHV
Fuel Fuel
or
W
η = elec (17-5)
EE ρ v LHV
Fuel Fuel Fuel
where Eq. (17-4) can be used when fuel consumption is measured as a mass flow rate,
and Eq. (17-5) can be used when fuel consumption is measured as a volumetric flow rate.
The prime mover efficiency (η ) is given by the relation
engine
W
η = engine (17-6)
engine Q
Fuel,engine
where W is the rotational mechanical power output of the engine (turbine or recip-
engine
rocating engine).
There are also losses from the electric generator, which ultimately dissipate as heat
losses through the generator casing and can be accounted for with the electric generator
efficiency:

W
η = elec (17-7)
engine W
engine
where W represents the mechanical shaft power output of the prime mover, which
engine
equals the mechanical power input to the electric generator. When a gearbox is used
between the prime mover and the electric generator, the electric generator efficiency
can be expressed as
W
η = elec (17-8)
generator W
gearbox
where W gearbox is the mechanical shaft power output from the gearbox to the generator.
In this case, the gearbox efficiency (η ) is the ratio of the mechanical shaft output of
gearbox
the gearbox to the mechanical shaft output of the prime mover, that is,
W
η = gearbox (17-9)
gearbox W
engine
The electrical generation efficiency can be expressed as the product of these three
component efficiencies, that is,
η = η η η (17-10)
EE engine gearbox generator